Free Printable Algebra 2 GT Final Review

1.

Will deposits $1650 for three years at 3% interest, compounded daily. What is his ending balance?

a)

$1,700.25

b)

$4,056.85

c)

$2,103.87

d)

$1,805.38

2.

log(4x)

a)

log4-logx

b)

log4+logx

c)

4logx

d)

xlog4

3.

log(xy²)

a)

logx+2logy

b)

logx+logy²

c)

logx-2logy

d)

logx+logy+log2

4.

$\log\left(\frac{x}{y}\right)$

a)

logx+logy

b)

xlogy

c)

log(x-y)

d)

logx-logy

5.

$\log\left(\frac{m^3}{n}\right)$

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

6.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

7.

Use multiple log properties to write as a single log:
log₂x - 5log₂y

a)

log₂(x/y⁵)

b)

log₂(xy⁵)

c)

log₂(x/y)⁵

d)

log₂(x/5y)

8.

a)

log (xy³)

b)

log (x⁶− y³)

c)

log (x⁶/y³)

d)

log (x⁶ + y³)

9.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

10.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

11.

$\log\left(\frac{8x}{yz}\right)\$

a)

log8+logx-logy-logz

b)

log8+logx-logy+logz

c)

log(8x)-log(yz)

d)

8logx-ylogz

12.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

13.

When you have two log expressions separated by a minus sign (-), we really need to ___________ them to simplify into one log expression.

a)

add

b)

subtract

c)

multiply

d)

divide

14.

When you have two log expressions separated by a plus sign (+), we really need to ___________ them to simplify into one log expression.

a)

add

b)

subtract

c)

multiply

d)

divide

15.

$\log\left(\frac{4}{5}\right)$ Expand the Log

a)

$\log4\ +\log5$

b)

$\log\ 20$

c)

$\log4\ -\log5$

16.

Expand the following logarithm:
log₂ 5x.

a)

log₂ 5 - log₂ x

b)

log₂ 5 + log₂ x

c)

2log 5 + 2log x

d)

log5 2 + log_x 2

17.

a)

6log₈(xyz)

b)

log₈(x) - log₈(y) - 6log₈(z)

c)

log₈(x) + log₈(y) - log₈(z)

d)

log₈(x) + log₈(y) + 6log₈(z)

18.

a)

log(x) + log(z) + 4log(y)

b)

3log(x) − log(z) − 4log(y)

c)

3log(x) + log(z) + 4log(y)

d)

log(x) − 4log(z) − 3log(y)

19.

Write as a single log: log 12 + 2 log x

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

20.

Simplify: 2log(x) + 3log(xy)

a)

log(x⁵y³)

b)

log(5xy)

c)

5log(x²y)

d)

log(6x²y)

21.

Expand

\log_5\left(\frac{12a}{2}\right)

a)

$\log_212a-\log_25$

b)

$\log_512a-\log_52$

c)

$\log_512-\log_5a-\log_52$

d)

$\log_512+\log_5a-\log_52$

22.

Write 6^x = 8 in log form.

a)

log₆ 8 = x

b)

log₈ 6 = x

c)

log₆ x = 8

d)

log₈ x = 6

23.

$Evaluate\ \log_864$

(a)

24.

$Evaluate\ \log_77$

(a)

25.

$Evaluate\ \log_61$

(a)

26.

$Evaluate\ \log_8\frac{1}{8}$

(a)

27.

Domain of y = log x ?

a)

(-∞, ∞)

b)

(0, ∞)

c)

[0, ∞)

d)

[-∞, ∞]

28.

Solve 8 = 2^5x+7

a)

⅘

b)

¼

c)

-⅘

d)

-¼

29.

5^3-2n = 125

a)

0

b)

5

c)

1

d)

5/3

30.

Solve for 'a' using logs, decimals are OK!

a)

A

b)

B

c)

C

d)

D

31.

Solve for n using logs: 7ⁿ⁺¹⁰- 8 = 6

a)

-7.374

b)

-8.643

c)

-7.360

d)

-8.853

32.

Solve for x using logs: 5(4)^x-2 - 29 = 6

a)

-.5609

b)

3.4036

c)

2.0674

d)

-1.0753

33.

Describe the transformation that occurred.

g(x) = f(x) + 2

a)

up 2 units

b)

left 2 units

c)

Vertical Stretch

d)

right 2 units

34.

Describe the transformation that occurred

g(x) = f(x + 3)

a)

Right 3 units

b)

Vertical Stretch

c)

Up 3 units

d)

Left 3 units

35.

Given g(x) = f(x-3) + 5. What transformations took place from the original function f(x)?

a)

Left 3 up 5

b)

Right 3 down 5

c)

Left 3 down 5

d)

Right 3 up 5

36.

The function $f\left(x\right)$ was reflected over the y-axis and vertically stretched with a scale factor of 5 and shifted 4 units down. Which rule describes this transformation?

a)

$g\left(x\right)=f\left(-5x\right)-4$

b)

$g\left(x\right)=5f\left(-x\right)+4$

c)

$g\left(x\right)=-5f\left(x-4\right)$

d)

$g\left(x\right)=5f\left(-x\right)-4$

37.

The function $f\left(x\right)$ was reflected over the x-axis and vertically stretched with a scale factor of 3 and shifted 8 units up. Which rule describes this transformation?

a)

$g\left(x\right)=f\left(-3x\right)+8$

b)

$g\left(x\right)=3f\left(-x\right)+8$

c)

$g\left(x\right)=-3f\left(x-8\right)$

d)

$g\left(x\right)=-3f\left(x\right)+8$

38.

Describe the transformations that maps f(x) to g(x) = - f(x + 6) - 10

a)

Reflect over y-axis
Shifted down 10 units
Shifted left 6 units

b)

Reflect over x-axis
Shifted up 10 units
Shifted left 6 units

c)

Reflect over y-axis
Shifted up 10 units
Shifted right 6 units

d)

Reflect over x-axis
Shifted down 10 units
Shifted left 6 units

39.

Describe the transformation from dotted to solid.

a)

g(x) = f(x + 5) + 3

b)

g(x) = f(x +3) + 5

c)

g(x) = f(x - 5) + 3

d)

g(x) = f(x - 3) + 5

40.

cosθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

41.

What is the radius of a unit circle?

a)

1

b)

2

c)

1/2

d)

0

42.

Which graph represents an angle in standard position with a measure of $\frac{\pi}{5}$ ?

a)

b)

c)

d)

43.

The terminal side of a 330° angle is in what Quadrant?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

44.

Positive angles are measured in which direction from standard position?

a)

Clockwise

b)

Counterclockwise

45.

What is 360 degrees in radians?

a)

2π/3

b)

5π/4

c)

2π

d)

π

46.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

47.

cos 5π/6

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

48.

tan 7π/4

a)

-1

b)

1

c)

√2/2

d)

undefined

49.

cos 4π/3

a)

-√3/2

b)

√3/2

c)

1/2

d)

-1/2

50.

sin 7π/6

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

51.

What is the exact coordinates of 3π/4 on the unit circle?

a)

(−√2∕2, √2∕2)

b)

(−√2∕2, −√2∕2)

c)

(−√3∕2, −√2∕2)

d)

(√2∕2, −√2∕2)

52.

What radian measure corresponds to the point

a)

π/4

b)

3π/2

c)

5π/4

d)

7π/3

53.

For what angles are sine and cosine the same?

a)

0^o

b)

45^oand 135⁰

c)

45^oand 225⁰

d)

45^oand 315⁰

54.

The period of a sine or cosine graph can be found by ....

a)

It's always 2π

b)

2π/B

c)

B(2π)

d)

2π+B

55.

The __________ represents half the distance between the max and min of a sine or cosine graph.

a)

Period

b)

Frequency

c)

Extreme Values

d)

Amplitude

56.

Which value represents a vertical shift in the following function y=a*sin(bx - c)+d?

a)

a

b)

b

c)

c

d)

d

57.

Sine or Cosine?

a)

y=sinx

b)

y=cosx

58.

Sine or Cosine?

a)

y=sinx

b)

y=cosx

59.

What is the period of
y= -3sin(x)

a)

π

b)

2π

c)

3π

d)

4π

60.

What is the midline for
y=2cos(1/3x +π/6) +2

a)

1/3

b)

-2

c)

+2

d)

4

61.

What is the amplitude of y = 3 cos 2x?

a)

3

b)

2

c)

90
90⁰

d)

350⁰

62.

What is the amplitude of the graph?

a)

$a=3$

b)

$a=6$

c)

$a=2$

d)

$a=4$

63.

What is the vertical shift, d, of the graph shown?

a)

$d=3$

b)

$d=2$

c)

$d=1$

d)

$d=2.5$

64.

What is the amplitude of the graph?

a)

$a=3$

b)

$a=6$

c)

$a=2$

d)

$a=4$

65.

What is the vertical shift, d, of the graph shown?

a)

$d=3$

b)

$d=2$

c)

$d=3.5$

d)

$d=2.5$

66.

Which equation represents the graph?

a)

$f\left(x\right)=3\cos x+2$

b)

$f\left(x\right)=3\sin x+2$

c)

$f\left(x\right)=2\cos x+3$

d)

$f\left(x\right)=2\sin x+3$

67.

Which equation represents the graph?

a)

$f\left(x\right)=\cos x+2$

b)

$f\left(x\right)=\sin x+2$

c)

$f\left(x\right)=2\sin x+1$

d)

$f\left(x\right)=2\cos x+1$

68.

What is the amplitude of this function?

a)

2

b)

2π

c)

-2

d)

1

69.

What is the resting value of this graph?

a)

y = -1

b)

y = -5

c)

y = -2.5

d)

y = -3

70.

What is the amplitude of the function $y\ =\ 5\sin2x$

a)

5

b)

2

c)

1/2

d)

1/5

71.

What is the resting value of this graph?

a)

y = -1

b)

y = 3

c)

y = 0

d)

y = 1

72.

What is the amplitude?

a)

1

b)

-1

c)

2

d)

-2

73.

What is the amplitude of this function?

a)

2

b)

-2

c)

3

d)

-3

74.

Identify the amplitude of the graph given.

a)

$2.5$

b)

$-2.5$

c)

$5$

d)

$\frac{\pi}{2}$

75.

Identify the amplitude of the graph given.

a)

$0.25$

b)

$0.5$

c)

$1.25$

d)

$0.75$

76.

Identify the resting value of the graph given.

a)

$y=\frac{1}{2}$

b)

$y=2$

c)

$y=-1$

d)

$y=0$

77.

Identify the amplitude of the graph given.

a)

$2$

b)

$1$

c)

$3$

d)

$1.5$

78.

Identify the amplitude of the graph given.

a)

$4$

b)

$-4$

c)

$2$

d)

$\frac{2\pi}{3}$

79.

Which of the following measures CANNOT be made from a box plot?

a)

Interquartile Range

b)

Mean

c)

Median

d)

Range

80.

Interview every 10th student who enters the school in the morning.

a)

simple random

b)

voluntary response

c)

systematic

d)

convenience

81.

Assign each car in a dealership a number and then use a random-number table to select the cars to be inspected.

a)

systematic

b)

simple random sample

c)

convenience

d)

Self - selected (volunteer)

82.

A teacher wants to know the average time spent doing homework by the students in her class of 20 girls and 5 boys.

She selects the five closest to her desk.

a)

simple random

b)

Self Selected.

c)

Convenience

d)

Systematic Random

83.

True or False: all samples lead to a good prediction about an entire population.

a)

True

b)

False

84.

In order to use samples to estimate something from the population, the sample should be _________________ the population.

a)

exactly the same as

b)

nothing like

c)

representative of

d)

larger than

85.

One group of subjects was given an herbal supplement and another group was given a placebo. After one year, the number of illnesses each group had was compared.

a)

Observational Study

b)

Experiment

86.

A researcher stood at a school parking lot entrance to see if the color of a car is related to the driver not wearing a seatbelt.

a)

Observational Study

b)

Experiment

87.

A professor finds that people who are obese have higher cholesterol levels than those who are not obese.

a)

Observational Study

b)

Experiment

88.

Four groups of randomly selected people are assigned a different diet. After six months, the blood pressures of each group are compared.

a)

Observational Study

b)

Experiment

89.

You want to see if students who have a 4.0 grade point average study more than those who do not.

a)

experiment

b)

observational study

90.

You want to compare the health of students who walk to school to the health of students who ride the bus

a)

experiment

b)

observational study

91.

A researcher randomly assigned boys and girls to each of two groups. One group was assigned to watch a violent television program while the other group watched a nonviolent program. The children's behavior was then recorded for incidences of aggressive behavior. This research method is best characterized as...

a)

experimental

b)

Observation

92.

A psychologist designed a study to test the effects of cell phone use on driving safety. Participants were randomly assigned either to drive an automobile simulator while talking to a friend on a cell phone or to drive a simulator without talking on a phone.

Which type of research does the scenario describe?

a)

Experiment

b)

Observation

93.

To test the effects of breakfast on grades I ask my students if they ate breakfast and then compare the breakfast eaters grades to the non-breakfast eaters.

This is an example of:

a)

Observational study

b)

Experiment

94.

Researchers wanted to know if there is a link between proximity to high-tension wires and the rate of leukemia in children. To conduct the study, researchers compared the rate of leukemia for children who lived within 1/2 mile of high-tension wires to the rate of leukemia for children who did not live within 1/2 mile of high-tension wires.

a)

Observational Study

b)

Experiment

95.

Rats with cancer are divided into two groups. One group receives 5 milligrams of a medication that is thought to fight cancer and the other receives 10 mg. After 2 years, the spread of cancer is measured.

a)

Observational Study

b)

Experiment

96.

Identify each of the following as an observational study or an experiment.

Determine if people who take vitamin C every day are less likely to get colds.

a)

Observational study

b)

Experiment

97.

The ages of the population of people living in the Atlanta area are normally distributed with a mean of 43 and a standard deviation of 14.

The town has a population of 5,000. How many would you expect to be aged between 29 and 57?

This Standard Normal Distribution curve may help you solve this problem.

a)

1750

b)

3860

c)

3400

d)

4330

98.

According to the empirical rule, what percentage of data falls within 1 standard deviation?

a)

25%

b)

68%

c)

95%

d)

99.7%

99.

According to the empirical rule, how much of the data falls within 3 standard deviations?

a)

25%

b)

68%

c)

95%

d)

99.7%

100.

What shape is a normal distribution curve?

a)

Half curve

b)

Round curve

c)

Bell curve

d)

Square curve

101.

The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5. What proportion of weeks would you expect to have less than 5 accidents?

a)

0.6915

b)

0.1762

c)

0.8238

d)

-0.93

102.

A town's average snowfall is 48 inches per year with a standard deviation of 6 inches. Using a Normal model, what values should border the middle 50% of the model?

a)

44 and 52 inches

b)

42 and 54 inches

c)

40 and 50 inches

d)

40 and 60 inches

103.

Snobby University accepts only those graduate students who score in the top 5% of the GRE (Graduate Requirements Exam).

Given that µ = 151.3 and σ = 8.7, what is the lowest score you can get and still be accepted to SU? Round to the nearest whole number.

a)

165

b)

166

c)

170

d)

162

104.

The normal curve is symmetrical about the mean.

a)

True

b)

False

105.

If I tell you that you scored at the 55th percentile on your final exam, you would know:

a)

55% of the class scored the same or worse than you did

b)

You earned a 55% on the exam

c)

You failed the exam

d)

45% of the class scored worse than you did

106.

A bank's loan officer rates applicants for credit. The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50. What percentage ratings can be expected to be between 200 and 275?

a)

43.31%

b)

56.71%

c)

38.61%

d)

29.87%

107.

The lengths of human pregnancies can be described by a Normal model with a mean of 268 days and a standard deviation of 15 days. What percentage of pregnancies will last at least 300 days?

a)

1.64%

b)

98.36%

c)

12.34%

d)

56.19%

108.

For a recent English exam, the mean was 73 points and the standard deviation was 9.2 points. Find the percent of scores over 85.

a)

9.61%

b)

90.39%

c)

28.51%

d)

75.31%

109.

What is the equation of this graph?

a)

y = sin x

b)

y = cos x

c)

y = tan x

Algebra 2 GT Final Review

Total questions: 109

Worksheet time: 8hrs 2mins

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